Effect of ridge-ridge interactions in crumpled thin sheets

Area of Science:

• Physics
• Materials Science
• Computational Science

Background:

• Existing models of crumpled sheets often use a single-ridge approximation.
• The influence of ridge-ridge interactions on energy scaling in real crumpled sheets remains incompletely understood.
• Previous simulations and experiments showed discrepancies in material-dependence for the power-law exponent.

Purpose of the Study:

• To investigate the revision of energy scaling in crumpled sheets due to ridge-ridge interactions.
• To resolve discrepancies between prior simulation and experimental findings.
• To establish new scaling relations for crumpled materials across a wide density range.

Main Methods:

• Utilized molecular dynamics simulations with modified protocols for enhanced data quality.
• Analyzed changes in average storing energy, bending-to-stretching energy ratios, and ridge characteristics during crumpling.
• Extended simulations to high-pressure regimes to explore broader density ranges.

Main Results:

• Identified a transition in average storing energy from a power-law (1/3 ridge length) to a linear relationship.
• Observed a decrease in the bending-to-stretching energy ratio from 5 to 2.
• Determined scaling laws for average ridge length (D^(-1/3)), ridge number (D^(2/3)), and energy per unit length (D^0.881), consistent with experiments and mean-field predictions.

Conclusions:

• Ridge-ridge interactions significantly revise energy scaling in crumpled sheets.
• The study resolves previous discrepancies in power-law exponent material dependence.
• A generalized scaling relation applicable to the entire density range, including high-pressure conditions, has been verified.